Answer:
Each fudge cookie has 80 calories.
Each lemon cream has 65 calories.
Step-by-step explanation:
We will let [tex]\ell[/tex] represent the calories in lemon creams and [tex]f[/tex] represent the calories in fudge cookies.
Two lemon creams and four fudge cookies together have 450 calories. So, we can write the following equation:
[tex]2\ell+4f=450[/tex]
And four lemon creams plus two fudge cookies together have 420 calories. So, we can write the following equation:
[tex]4\ell+2f=420[/tex]
We now have a system of equations. We can solve this by elimination.
For the first equation, we can multiply both sides by -2. This way, the [tex]\ell[/tex] will cancel when we add the two equations together.
So, the first equation becomes:
[tex]-4\ell-8f=-900[/tex]
Add this to the second equation. Hence:
[tex](-4\ell+4\ell)+(-8f+2f)=(-900+420)[/tex]
Simplify:
[tex]-6f=-480[/tex]
Divide both sides by -6. Hence:
[tex]f=80[/tex]
So, there are 80 calories in one cookie.
We can use the first equation again to find the amount of calories in one cream. We have:
[tex]2\ell+4f=450[/tex]
Substituting 80 for [tex]f[/tex] yields:
[tex]2\ell+320=450[/tex]
Then it follows that:
[tex]\ell=65[/tex]
So, there are 65 calories in each lemon cream.
